🧠 ML From Scratch Lab

Implementing Machine Learning from First Principles with NumPy

Vision • Features • Architecture • Installation • Quick Start • Learning Path • Core Modules • Math • Experiments • Performance • Contributing • License

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📖 Project Vision

Why build from scratch?
In an era of high-level APIs and auto-ML, the fundamental mechanisms of machine learning are often obscured. This lab exists to peel back the layers—to implement every algorithm, every optimization step, and every backpropagation pass with transparent, readable code. It is a research-grade educational repository for those who believe that true understanding comes from building.

Educational & Research Goals

• Provide a self-contained curriculum that progresses from linear algebra foundations to transformer architectures.
• Serve as a reference implementation for researchers prototyping new ideas without heavy framework dependencies.
• Demonstrate engineering best practices in a research context: modular design, comprehensive testing, and reproducible benchmarks.
• Foster a community of learners who can experiment, extend, and share their insights.

Engineering Philosophy

• Mathematical Transparency: Every equation in a paper should map directly to a line of code.
• Performance Awareness: Write efficient NumPy code without sacrificing clarity.
• Educational First: Code is documentation; notebooks are tutorials.

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✨ Feature Highlights

Icon	Feature	Description
🧮	Pure NumPy Implementations	No black boxes—everything from linear regression to multi-head attention is built with np.dot, np.einsum, and manual gradients.
📉	Gradient-Based Optimization	Implement SGD, Momentum, Adam, and more with explicit gradient computation and optional autodiff for educational clarity.
🧠	Deep Learning Foundations	Modular layers (Dense, Conv1D, RNN, LSTM), activation functions, loss functions, and backpropagation through time.
🔍	Transformer Basics	Scaled dot-product attention, positional encoding, encoder/decoder blocks—all from scratch, ready for experimentation.
🔬	Research Experiments	Easily swap components, log metrics, and compare convergence against reference libraries.
⚡	Benchmarking vs. sklearn	Automated tests assert numerical correctness and performance parity with scikit-learn’s reference implementations.
🧪	Comprehensive Testing	Unit tests, integration tests, and gradient checks ensure reliability.
📚	40+ Jupyter Notebooks	A structured learning path from math foundations to advanced topics.
🐍	Pythonic & Modular	Clean, object-oriented design that follows industry best practices.
📊	Visual Learning	Every notebook includes rich visualizations of loss landscapes, decision boundaries, and attention maps.
🧩	Modular Components	Easily swap optimizers, activation functions, or regularizers to observe effects.

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📂 Repository Architecture

graph TB
    subgraph "Repository Root"
        direction TB
        A[.github/] --> A1[workflows/]
        A1 --> A2[test.yml]
        A1 --> A3[notebooks.yml]
        A1 --> A4[docs.yml]
        
        B[notebooks/] --> B1[00_mathematical_foundations]
        B --> B2[01_linear_models]
        B --> B3[02_tree_models]
        B --> B4[03_neural_networks]
        B --> B5[04_transformers]
        B --> B6[05_experiments]
        
        C[src/ml_from_scratch/] --> C1[core/]
        C --> C2[optimizers/]
        C --> C3[models/]
        C --> C4[neural/]
        C --> C5[datasets/]
        C --> C6[utils/]
        
        D[tests/]
        E[benchmarks/]
        F[examples/]
        G[configs/]
        H[docs/]
        I[scripts/]
        
        J[.gitignore]
        K[LICENSE]
        L[README.md]
        M[CONTRIBUTING.md]
        N[CODE_OF_CONDUCT.md]
        O[CHANGELOG.md]
        P[pyproject.toml]
        Q[setup.cfg]
        R[requirements.txt]
        S[requirements-dev.txt]
    end

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Directory Details

Path	Description
.github/workflows/	CI/CD pipelines: test, notebook validation, doc deployment
notebooks/	Interactive learning path (40+ Jupyter notebooks)
src/ml_from_scratch/	Core library (installable package)
tests/	Unit & integration tests
benchmarks/	Performance & correctness benchmarks against scikit-learn
examples/	Standalone usage scripts
configs/	YAML configuration files for experiments
docs/	Sphinx documentation source
scripts/	Utility scripts (data download, benchmark runner)

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⚙️ Installation

Prerequisites

• Python 3.9 or later
• pip (Python package manager)
• (Optional) virtualenv or conda for environment management

Step-by-Step Installation

1. Clone the Repository

git clone https://github.com/ammmanism/ml-from-scratch-lab.git
cd ml-from-scratch-lab

2. Create and Activate a Virtual Environment (Recommended)

Windows

python -m venv venv
venv\Scripts\activate

macOS/Linux

python3 -m venv venv
source venv/bin/activate

3. Install the Package in Editable Mode

pip install -e .

4. Install Development Dependencies (Optional, for Testing/Benchmarks)

pip install -r requirements-dev.txt

5. Verify Installation

python -c "from ml_from_scratch import __version__; print(__version__)"

Docker (Alternative)

docker build -t ml-from-scratch-lab .
docker run -it --rm -p 8888:8888 ml-from-scratch-lab

Google Colab

Click the "Open in Colab" badge at the top to run notebooks directly in your browser with zero setup.

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🚀 Quick Start

Linear Regression from Scratch

from ml_from_scratch.models import LinearRegression
from ml_from_scratch.datasets import make_regression
from ml_from_scratch.utils import train_test_split

# Generate synthetic data
X, y = make_regression(n_samples=100, n_features=5, noise=0.1)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)

# Train model
model = LinearRegression()
model.fit(X_train, y_train, lr=0.01, epochs=1000, verbose=False)

# Predict
predictions = model.predict(X_test)
mse = ((predictions - y_test) ** 2).mean()
print(f"Test MSE: {mse:.4f}")

Logistic Regression for Classification

from ml_from_scratch.models import LogisticRegression
from ml_from_scratch.datasets import make_classification
from ml_from_scratch.metrics import accuracy_score

X, y = make_classification(n_samples=200, n_features=10, n_classes=2)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)

model = LogisticRegression()
model.fit(X_train, y_train, lr=0.1, epochs=500)
y_pred = model.predict(X_test)
print("Accuracy:", accuracy_score(y_test, y_pred))

Multilayer Perceptron (MLP) on MNIST

from ml_from_scratch.neural import Model, Dense, ReLU, Softmax
from ml_from_scratch.optimizers import Adam
from ml_from_scratch.losses import CrossEntropy
from ml_from_scratch.datasets import load_mnist

# Load data (or use synthetic)
X_train, y_train, X_test, y_test = load_mnist(normalize=True)

# Build model
model = Model()
model.add(Dense(128, input_dim=784))
model.add(ReLU())
model.add(Dense(64))
model.add(ReLU())
model.add(Dense(10))
model.add(Softmax())

# Compile
model.compile(optimizer=Adam(learning_rate=0.001),
              loss=CrossEntropy())

# Train
model.fit(X_train, y_train, epochs=10, batch_size=32, validation_split=0.1)

# Evaluate
y_pred = model.predict(X_test)
print("Test Accuracy:", accuracy_score(y_test, y_pred))

Simple Transformer Block

from ml_from_scratch.neural.layers import MultiHeadAttention, FeedForward
import numpy as np

# Example sequence: batch=2, seq_len=5, dim=16
x = np.random.randn(2, 5, 16)

# Multi-head attention (8 heads)
mha = MultiHeadAttention(d_model=16, num_heads=8)
attn_out = mha(x, x, x)  # self-attention

# Feed-forward network
ffn = FeedForward(d_model=16, d_ff=64)
out = ffn(attn_out)

print(out.shape)  # (2, 5, 16)

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📘 Learning Path

Explore the notebooks in the recommended order. Each notebook builds on the previous one, forming a cohesive learning journey.

graph LR
    subgraph "00 Math Foundations"
        A1[01_vectors_matrices.ipynb] --> A2[02_eigenvalues_svd.ipynb]
        A2 --> A3[03_probability_distributions.ipynb]
        A3 --> A4[04_calculus_gradients.ipynb]
    end
    subgraph "01 Linear Models"
        B1[01_linear_regression.ipynb] --> B2[02_logistic_regression.ipynb]
        B2 --> B3[03_regularization.ipynb]
    end
    subgraph "02 Tree Models"
        C1[01_decision_trees.ipynb] --> C2[02_random_forests.ipynb]
        C2 --> C3[03_gradient_boosting.ipynb]
    end
    subgraph "03 Neural Networks"
        D1[01_backpropagation.ipynb] --> D2[02_mlp.ipynb]
        D2 --> D3[03_cnn.ipynb]
        D3 --> D4[04_rnn_lstm.ipynb]
    end
    subgraph "04 Transformers"
        E1[01_attention.ipynb] --> E2[02_transformer_implementation.ipynb]
        E2 --> E3[03_positional_encoding.ipynb]
    end
    subgraph "05 Experiments"
        F1[01_hyperparameter_tuning.ipynb]
        F2[02_ablation_studies.ipynb]
        F3[03_gradient_flow_analysis.ipynb]
    end

    A4 --> B1
    B3 --> C1
    C3 --> D1
    D4 --> E1
    E3 --> F1
    F1 --> F2
    F2 --> F3

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Notebook Details

Notebook	Topic	Key Concepts	Link
00_01	Vectors & Matrices	Norms, dot product, linear transformations	Open
00_02	Eigenvalues & SVD	Spectral theorem, PCA intuition	Open
00_03	Probability Distributions	Gaussian, Bernoulli, MLE	Open
00_04	Calculus & Gradients	Partial derivatives, chain rule, Jacobians	Open
01_01	Linear Regression	Closed-form, gradient descent, R²	Open
01_02	Logistic Regression	Sigmoid, cross-entropy, decision boundary	Open
01_03	Regularization	Ridge, Lasso, ElasticNet	Open
02_01	Decision Trees	Entropy, information gain, pruning	Open
02_02	Random Forests	Bagging, feature importance	Open
02_03	Gradient Boosting	AdaBoost, XGBoost intuition	Open
03_01	Backpropagation	Chain rule, computational graph	Open
03_02	Multilayer Perceptron	MLP, activation functions, initializations	Open
03_03	Convolutional Networks	Convolution, pooling, receptive fields	Open
03_04	RNN & LSTM	Recurrent cells, backprop through time	Open
04_01	Attention Mechanism	Scaled dot-product, multi-head	Open
04_02	Transformer from Scratch	Encoder-decoder, positional encoding	Open
04_03	Positional Encoding	Sinusoidal, learned embeddings	Open
05_01	Hyperparameter Tuning	Grid search, random search, Bayesian opt	Open
05_02	Ablation Studies	Removing components, measuring impact	Open
05_03	Gradient Flow Analysis	Vanishing/exploding gradients, visualization	Open

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🧠 Core Modules

core/ – Autodiff and Parameter Management

• autodiff.py: A minimal computational graph for automatic differentiation (educational, not for production). Supports forward/backward passes with dynamic graph building.
• parameter.py: Wrapper for trainable parameters with gradient storage. Supports parameter sharing and gradient accumulation.
• initializers.py: Xavier, He, random normal/uniform initializations.

optimizers/ – Gradient-Based Optimizers

• SGD: Stochastic gradient descent with momentum (Nesterov optional).
• Adam: Adaptive Moment Estimation with bias correction.
• RMSprop: Root Mean Square Propagation.
• Adagrad: Adaptive gradient algorithm.
• LearningRateSchedulers: Step decay, exponential decay, cosine annealing.

models/ – High-Level APIs

• LinearRegression, LogisticRegression: Ordinary and logistic regression with L1/L2 regularization.
• DecisionTreeClassifier, DecisionTreeRegressor: CART algorithm with entropy/Gini.
• RandomForestClassifier, RandomForestRegressor: Ensemble of trees with bagging.
• GradientBoostingClassifier: Gradient boosted trees (simplified).
• Sequential: Container for neural network layers.

neural/ – Deep Learning Building Blocks

Layers

Layer	Description
Dense	Fully connected layer with configurable activation
Conv2D	2D convolution with stride, padding, dilation
MaxPooling2D	Max pooling
Flatten	Flattens input
RNN	Recurrent layer with tanh activation
LSTM	Long Short-Term Memory cell
Embedding	Token embedding layer
MultiHeadAttention	Scaled dot-product attention with multiple heads
FeedForward	Position-wise FFN used in transformers

Activations

• ReLU, LeakyReLU, ELU, Sigmoid, Tanh, Softmax

Losses

• MSE, MAE, CrossEntropy, BinaryCrossEntropy, KLDivergence, HuberLoss

Regularization

• Dropout, BatchNormalization, L1L2Regularizer

datasets/ – Synthetic Data Generators

• make_regression, make_classification, make_blobs, make_circles, make_moons
• load_mnist, load_cifar10, load_fashion_mnist (auto-download)
• TimeSeriesGenerator for RNN/LSTM data (sine wave, AR process)

utils/ – Helpers

• train_test_split, batch_iterator
• accuracy_score, precision_recall_fscore, confusion_matrix, roc_auc_score
• normalize, standardize, one_hot_encode, to_categorical
• visualize_decision_boundary, plot_loss_curve, plot_confusion_matrix

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📐 Mathematical Foundations

Every implementation is accompanied by rigorous mathematical documentation. Key formulas are directly translated into code:

Concept	Equation	Code
Linear Regression (closed-form)	$\hat{\beta} = (X^T X)^{-1} X^T y$	beta = np.linalg.inv(X.T @ X) @ X.T @ y
Gradient of MSE	$\nabla_{\beta} \text{MSE} = \frac{2}{n} X^T (X\beta - y)$	grad = (2/n) * X.T @ (X @ beta - y)
Backpropagation for Dense layer	$\delta^{(l)} = (W^{(l+1)T} \delta^{(l+1)}) \odot \sigma'(z^{(l)})$	delta = (W_next.T @ delta_next) * activation_derivative(z)
Attention Scores	$\text{Attention}(Q,K,V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V$	scores = np.einsum('bqd,bkd->bqk', Q, K) / np.sqrt(d_k) attn = softmax(scores) out = np.einsum('bqk,bkd->bqd', attn, V)
Adam Update	$m_t = \beta_1 m_{t-1} + (1-\beta_1)g_t$ $v_t = \beta_2 v_{t-1} + (1-\beta_2)g_t^2$ $\hat{m}_t = m_t / (1-\beta_1^t)$ $\hat{v}t = v_t / (1-\beta_2^t)$ $\theta{t+1} = \theta_t - \alpha \hat{m}_t / (\sqrt{\hat{v}_t} + \epsilon)$	See optimizers/adam.py

For deeper dives, refer to the notebooks/00_mathematical_foundations/ series, which includes:

• Visualizations of eigenvectors and SVD.
• Interactive probability distributions.
• Gradient descent on 2D loss surfaces.

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🔬 Experiments & Benchmarks

Benchmarking against scikit-learn

The benchmarks/ directory contains scripts to compare our implementations with scikit-learn on metrics, speed, and memory usage. Run a benchmark:

python benchmarks/compare_logistic_regression.py --samples 10000 --features 100 --epochs 100

Sample output:

Scikit-learn LogisticRegression: Accuracy = 0.876, Time = 0.23s
Our LogisticRegression:           Accuracy = 0.875, Time = 0.41s
Difference: 0.001 (within tolerance ✓)

Convergence Analysis

We also provide scripts to generate convergence plots comparing different optimizers:

xychart-beta
    title "Convergence of Optimizers on MNIST (MLP)"
    x-axis ["Epoch 0", "Epoch 25", "Epoch 50", "Epoch 75", "Epoch 100"]
    y-axis "Loss" 0 --> 2.5
    line "SGD" [2.3, 1.2, 0.8, 0.6, 0.5]
    line "Momentum" [2.3, 0.9, 0.5, 0.3, 0.2]
    line "Adam" [2.3, 0.7, 0.3, 0.15, 0.1]

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Note: The above chart is a static representation. Actual interactive plots are available in benchmarks/convergence_plots/.

Experimental Notebooks

The notebooks/05_experiments/ folder contains in-depth studies:

Experiment	Description	Key Findings
01_hyperparameter_tuning.ipynb	Grid search vs random search for MLP	Random search is 3x faster for same performance
02_ablation_studies.ipynb	Remove dropout, batch norm, skip connections	Dropout critical for generalization; skip connections enable deeper nets
03_gradient_flow_analysis.ipynb	Visualize gradient norms in deep networks	Vanishing gradients appear after 5 layers with sigmoid; ReLU mitigates

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⚡ Performance & Validation

Correctness

• Unit Tests: pytest runs over 200 tests covering:
  • Gradient checks (finite difference).
  • Shape consistency.
  • Equality to scikit-learn on small datasets.
• Continuous Integration: GitHub Actions run tests on every push and PR.
• Coverage: Maintains >90% code coverage.

Speed

• We vectorize operations using NumPy's optimized C backend.
• Memory usage is monitored with memory_profiler.
• For large-scale experiments, consider using the optional cupy backend (in development).

Benchmark Results (as of v1.0)

Model	Dataset (size)	sklearn time	our time	speed ratio
Linear Regression	Boston (506,13)	0.002s	0.003s	0.67x
Logistic Regression	Digits (1797,64)	0.12s	0.18s	0.67x
Random Forest (10 trees)	Wine (178,13)	0.08s	0.15s	0.53x
MLP (2 hidden, 100 units)	MNIST (60000,784)	5.2s	8.1s	0.64x
Transformer (1 block)	IMDB (5000,100)	1.8s	2.4s	0.75x

Our implementations are typically 0.5x–0.75x the speed of highly optimized libraries – a reasonable tradeoff for transparency and educational value.

Memory Usage

pie title Memory Usage (MNIST MLP)
    "Parameters" : 45
    "Activations" : 30
    "Gradients" : 20
    "Overhead" : 5

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🤝 Contributing

We welcome contributions from everyone! Whether you're fixing a bug, adding a new model, improving documentation, or suggesting an experiment, your help is appreciated.

How to Contribute

1. Fork the repository.
2. Create a branch (git checkout -b feature/amazing-model).
3. Write tests for your changes.
4. Ensure code quality:

   black src/ tests/
   flake8 src/ tests/
   pytest tests/

5. Commit (git commit -m 'Add amazing model').
6. Push (git push origin feature/amazing-model).
7. Open a Pull Request with a clear description.

Code Style

• Follow PEP 8.
• Use Black for formatting (line length 88).
• Write docstrings in Google format.

Adding a New Model

• Place the model in the appropriate subdirectory under src/ml_from_scratch/.
• Inherit from BaseModel if applicable.
• Implement fit and predict methods.
• Add unit tests in tests/.
• Create a notebook in notebooks/05_experiments/ demonstrating usage.

See CONTRIBUTING.md for full details.

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💬 Community & Support

• Discord: Join our server for real-time discussions.
• Twitter: Follow @mlscratchlab for updates.
• GitHub Discussions: Ask questions, share ideas, or show off your experiments in the Discussions tab.
• Issues: Report bugs or request features via GitHub Issues.

Code of Conduct

Please note that this project adheres to the Contributor Covenant Code of Conduct. By participating, you are expected to uphold this code.

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📄 License & Citation

License

This project is licensed under the MIT License – see the LICENSE file for details.

Citation

If you use this repository in your research or teaching, please cite it as:

@misc{ml-from-scratch-lab,
  author = {Amman Hussain Ansari},
  title = {ML From Scratch Lab: Implementing Machine Learning from First Principles with NumPy},
  year = {2025},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/ammmanism/ml-from-scratch-lab}}
}

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🌟 Star History

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If you find this project valuable, please consider giving it a ⭐ on GitHub!
Happy learning, and may your gradients always converge! 🚀

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